An A6000 is 285 grams. A D5300 is 479 grams. A D7100 is 765 grams. The A6000 is somewhere between the two in terms of controls and quality (probably closer to the D7100 overall). I'm really not sure how you'd call that 'not a huge savings' -- a D5300 is 1.7x as heavy, while a D7100 is about 2.7x as heavy.

Effectively, you save the weight of the mirrorbox and pentamirror/pentaprism. That's a big difference. Lenses are, of course, comparable. Does overall system weight change? It depends on the weight of the lenses. Shooting with a small prime, mirrorless will cream dSLR for weight. With a Sigma 200-500mm f/2.8, the total weight will be identical.

Sony A6000 is not 285g, but 344g per dpreview here. D5300 is 480g, so the savings is 136g, about 1/3 lbs. The charts are pretty clear how much savings there is. Most of the lens are about the same weight. If you go with SL1, the saving is only 63g. That is slightly more than my car keys! Not that much really.

This isn't right and the difference with/without battery isn't being taken into consideration

D5300 body-only with battery and card is 532 grams

A6000 body-only with battery and memory card is 344 grams (remove the battery and you get to the 285g)

So the difference is 188 grams. Now let's look at the kit lens differences:

Nikon 18-55 VR II: 195 grams

Sony 16-50pz: 116 grams

Difference: 79 grams

Total weight difference with batteries and kit lenses: 267 grams or .58 lbs. which is a normal steak at a restaurant and quite a bit more than a set of car keys, not to mention the huge size difference.